A heatsink including an electromagnetic bandgap structure reduces electromagnetic interference caused by an integrated circuit in an electronic device. One embodiment provides a heatsink having a base with an array of electrically-conductive, thermally-conductive patches spaced apart in two dimensions of a reference plane and having a thickness perpendicular to the reference plane. The patches are interconnected by a plurality of branches. Each branch connects adjacent patches and has a width in the reference plane of less than a width of each adjacent patch. A plurality of thermally conductive cooling fins coupled to a surface of the base and extend normal to the reference plane. The cooling fins may be formed of a thermally-conductive, electrically non-conductive material or may be coupled to the base by a thermally-conductive, electrically non-conductive material. The periodically patterned structure of the base, together with a solid metal layer of a circuit board, form an electromagnetic bandgap structure that reduces certain frequencies of electromagnetic noise caused by the integrated circuit.